Dynamics of all-optical switching in polymethine dye molecules

Thin Solid Films 477 (2005) 42 – 47 www.elsevier.com/locate/tsf

Dynamics of all-optical switching in polymethine dye molecules Parag Sharma, Sukhdev Roy*, C.P. Singh1 Department of Physics and Computer Science, Dayalbagh Educational Institute (Deemed University), Agra 282005, India Available online 27 October 2004

Abstract All-optical switching has been analyzed in the recently reported Polymethine dye (2-[2-[3-[(1,3-dihydro-3,3-dimethyl-1-phenyl-2H-indol2-ylidene)ethylidne]-2-phenyl-1-cyclohexene-1-yl] ethenyl]-3,3-dimethyl-1-phenylindolium perchlorate) (PD3) [O.V. Przhonska, D.J. Hagan, E. Novikov, R. Lepkowicz, E.W.V. Stryland, M.V. Bondar, Y.L. Slominsky, A.D. Kachkovski, Chem. Phys. 273 (2001) 235.] that exhibits large excited-state absorption, using the rate equation approach, to achieve high contrast and fast switching. The transmission of a cw probe laser beam (I p) at 532 nm through PD3 dissolved in (i) ethanol and (ii) polyurethane acrylate (PUA), is switched by a pulsed pump laser beam at 532 and 650 nm, respectively, which excite molecules from the ground state. The theoretical results show good agreement with the reported experimental results for case (i). The switching characteristics have been shown to be sensitive to variation in concentration, pump pulse width (Dt), peak pumping intensity (I m0 V ), absorption cross-section of the excited-state at 532 nm and lifetime of excited-state (s 1). The same switching contrast can be achieved at relatively lower pump powers at 650 nm for case (ii). It is shown that there is an optimum value of concentration at which maximum modulation can be achieved. We can get 96% modulation of I p at I m0 V =1 GW/cm2 at 650 nm, with Dt=30 ps and concentration of 0.14 mM in PUA, resulting in switch off and on time of 95 ps and 18 ns, respectively. The results have also been used to design all-optical NOT and the universal NOR and NAND logic gates with multiple pump laser pulses, which are the basic building blocks of computing circuits. D 2004 Elsevier B.V. All rights reserved. Keywords: Polymethine dye; All-optical switching; Excited-state absorption; Optical computing

1. Introduction Recent years have witnessed dramatic progress in the design of all-optical switching devices for ultrafast high bandwidth optical communication and computing [1]. A switch is the basic building block of information processing systems. The key element in an all-optical switch is a nonlinear optical material. Current interest has focused on novel materials that exhibit an efficient nonlinear optical response and offer advantages of small size and weight, high intrinsic speed, low propagation delay and power dissipation and the ability to tailor properties for device applications [2–4]. * Corresponding author. Tel.: +91 562 2121545; fax: +91 562 2121226. E-mail address: [email protected] (S. Roy). 1 Present address: Ultrafast Studies Section, Centre for Advanced Technology, Indore 452013, India. 0040-6090/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2004.08.109

Recently, organic molecules have emerged as excellent materials for molecular photonic applications, especially all-optical switching, due to their unique advantages and the ability to process them with conventional devices [5– 18]. Polymethine dyes (PDs) in liquid solutions and polymeric media have been extensively studied as promising materials for laser and optoelectronic applications [12– 14]. Recently, PDs have been shown to exhibit strong transient reverse saturable absorption, where the absorption cross-section of the excited states is much larger than that of the ground state [12,13]. For instance, for the PD3 dye (2-[2-[3-[(1,3-dihydro-3,3-dimethyl-1-phenyl-2H-indol-2ylidene)ethylidne]-2-phenyl-1-cyclohexene-1-yl]ethenyl]-3, 3-dimethyl-1-phenylindolium perchlorate) dissolved in ethanol, the ratio of absorption cross-section of excited state to ground state has been shown to be as large as 200, at 532 nm [12,13]. The photophysical properties of these dyes can be systematically modified by changing their molecular structure.

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In this paper, we theoretically analyze all-optical switching in PD3 and investigate the conditions for high contrast and fast switching. The transmission of a cw probe laser beam at 532 nm has been analyzed for two cases (i) PD3 in ethanol switched by a pulsed pump laser beam at 532 nm [12] and (ii) PD3 in polyurethane acrylate (PUA) switched by a pulsed pump beam at 650 nm, based on nonlinear excited state absorption. The switching characteristics have been analyzed using the rate equation approach [11,15–18]. The effect of various parameters such as concentration of dye molecules, pump pulse width (Dt), peak pumping intensity (I Vm0), absorption cross-section of the excited state at 532 nm (r 12) and lifetime of excited state (s 1) on switching have been analyzed in detail. Further, the results have been used to design all-optical NOT and the universal NOR and NAND logic gates that are the basic building blocks of computing circuits.

2. Theoretical model We consider a medium containing PD3 molecules exposed to a light beam of intensity I Vm, which modulates the population densities of different states through the excitation and de-excitation processes. These light-induced population changes can be described by the rate equations in terms of the photo-induced and thermal transitions of different levels as [12], d dt

N0 N1 N2

! ¼

 Im r01 Im r01 0

s1 1  ðIm r12 þ s1 1 Þ Im r12

0 s1 2  s1 2

!

N0 N1 N2

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3. Results and discussion The optical switching characteristics, namely the normalized transmitted probe intensity (NTPI) as a function of time have been obtained by computer simulations using Eqs. (1)–(3), for both cases (i) and (ii), considering a sample thickness of 2 mm and pump pulsed width [12] for both cases Dt=30 ps. The absorption cross-sections and relaxation times used in the computations are for case (i): r 01=1.51018 cm2, r 12=3.01016 cm2 both at 532 nm, s 1=1.0 ns and s 2=1.8 ps and for case (ii): r 01=501018 cm2, r 12=251018 cm2 both at 650 nm and r 01= 2.01018 cm2, r 12=3.01016 cm2 at 532 nm, s 1=2.5 ns and s 2=2.0 ps [12]. The transmitted intensity of the probe beam which is initially high (switch on state) due to lower linear absorption is switched low (switch off state) when a pulsed laser beam pumps the sample, enhancing the population of excited state. The switching characteristics are sensitive to the concentration of PD3 dye molecules. The effect of variation of concentration on switching characteristics for both cases is as shown in Fig. 1. An increase in the concentration results in greater absorption of the probe beam by the ground state, and hence, decreases in the initial transmission in absence of pump beam, as shown in Fig. 1(b). In the

!

ð1Þ where N 0, N 1 and N 2 are the population densities of S0, S1 and S2 states, respectively; r 01 and r 12 are the absorption cross-section of S0YS1 and S1YS2 transitions, respectively; s i is the lifetime of Si state and I m is the photon density flux of the modulating pump beam, i.e. ratio of the intensity I mV to the photon energy hm. The modulating pump laser pulse is given by [15–18]   2  t  tm ImV ¼ Im0 V exp  c ð2Þ Dt where I Vm0 is the peak pumping intensity, c=4 ln 2 is the pulse profile parameter, t m has been considered to be 65 ps and Dt is the pulse width. We consider the transmission of a cw probe laser beam of intensity I p, (I pbI Vm) at 532 nm through PD3 for both case (i) and case (ii), respectively. The propagation of the probe beam is governed by   dIp ¼  r01p N0 ðIm Þ þ r12p N1 ðIm Þ Ip dx

ð3Þ

where x is the distance in the medium and r 01p and r 12p are the absorption cross-sections of S0 and S1 states at probe wavelength.

Fig. 1. Variation of NTPI at 532 nm with time for different concentrations of PD3, (a) case (i) with I m0 V =10 GW/cm2 (dashed lines) and case (ii) with I m0 V =1 GW/cm2 (solid lines). (b) A magnified view of initial variation.

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presence of the pump pulse, the transmission of the probe beam switches from the initial high state to the low state due to excited-state absorption. The percentage modulation initially increases with increase in concentration and after a particular value, decreases on further increase. The optimum value of concentration for case (i) is 196 AM for which the maximum modulation of probe beam at 532 nm is 95.83%, with I m0 V =10 GW/cm2 at 532 nm. For case (ii), the optimum concentration is 142 AM for which a maximum modulation of 95.99% can be achieved with I m0 V =1 GW/ cm2 at 650 nm. The optimum value of concentration decreases as I m0 V increases for both cases. For instance, in case (ii) the optimum values of concentration are 286 AM (91.81%) and 140 AM (96.02%) for I Vm0=0.1 and 10 GW/ cm2, respectively. Hence there exists an optimum value of concentration for maximum modulation of the probe beam for a particular value of pump intensity. The switching characteristic at concentration of 10.3 AM for case (i) as shown explicitly by the dashed lines corresponding to 10.3 AM concentration in Fig. 1(a) and (b) are in good agreement with the reported experimental curves [12]. The effect of pump pulse width (Dt) on switching characteristics for both cases (i) and (ii) at respective optimum concentrations of 275 and 150 AM, at I m0 V =5 and 0.5 GW/cm2, respectively, is shown in Fig. 2. The switch on/off time and percentage modulation increase with increase in Dt, with the modulation level saturating after a certain value, for both cases. For instance, for case (i), for Dt=12 ps and 30 ps, the switch off time is 44 and 108 ps, respectively, whereas the switch on time is ~7 ns. The percentage modulation for these pulses is 84.60% and 94.13%, respectively. For case (ii), for Dt=12 and 30 ps, the switch off time is 47 and 92 ps, respectively, and switch on time is 15 ns. The switching contrast for these pulses is 93.42% and 95.74%, respectively. The switching time for case (i) is relatively small due to smaller s 1 value [12]. We

can get the same percentage modulation at relatively lower pump intensities by using the pump at a wavelength at which the ratio of excited to ground state absorption crosssection (c=r 12/r 01) is smaller than one. Fig. 3 shows the effect of variation in peak pump intensity (I m0 V ) on the switching characteristics for both case (i) and (ii). The percentage modulation increases with increase in I m0 V as it results in increase in the number of excited molecules and after a particular value of I m0 V , it saturates. For case (i), for I m0 V =1.05 GW/cm2 at 532 nm, the probe beam is modulated by 64.45% with off and on time of 87 ps and 6 ns, respectively. At I m0 V =7 GW/cm2, the probe beam is modulated by 94.98% with off–on time ~104 ps and 8 ns, respectively. For case (ii), percentage modulation saturates at 96%, for peak pump intensity value 1 GW/cm2, with off and on time of 95 ps and 18 ns, respectively. At higher pump intensities as shown in inset of Fig. 3, the NTPI switches to the off state after which it increases to a maxima and again decreases to the low state. This is due to increased absorption of the pump beam by excited state as has also been observed experimentally for squarylium dye [12]. It is clear from Fig. 3 that the same switching contrast can be achieved at relatively lower I m0 V values for case (ii). By considering the pump beam at a wavelength corresponding to smaller value of c, higher modulation can be achieved at relatively lower pump powers due to increased absorption of pump by S0 state that results in higher population of S1 state. Hence, considering the pump beam at 770 nm that corresponds to the peak absorption of ground state can result in higher modulation provided the excited state has negligible absorption at 770 nm. Complete switching (i.e. 100% modulation), can be achieved if the ground state does not absorb the probe beam [15–18]. The kinetic and spectral properties of PDs can be altered through different techniques such as chemical substitution

Fig. 2. Variation of NTPI at 532 nm with time for different pump pulse width (Dt) values: case (i) with PD3 concentration of 275 AM for I m0 V =5.0 GW/cm2 (dashed lines) and case (ii) PD3 concentration of 150 AM, for I m0 V =0.5 GW/cm2 (solid lines). The inset shows a magnified view of initial variation.

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Fig. 3. Variation of NTPI at 532 nm with time for different peak pump intensity (I m0 V ) values at Dt=30 ps, case (i) with PD3 concentration of 258 AM at I m0 V =(i) 0.21 GW/cm2, (ii) 1.05 GW/cm2, (iii) 1.95 GW/cm2, (iv) 7.0 GW/cm2 and (v) 50 GW/cm2 (dashed lines) and case (ii) with PD3 concentration of 140 AM at V =(a) 0.01 GW/cm2, (b) 0.05 GW/cm2, (c) 0.10 GW/cm2, (d) 1.0 GW/cm2 and (e) 30 GW/cm2 (solid lines). The inset shows a magnified view at lower time I m0 range and dotted line shows the input pump pulse profile (I m) for both cases.

and variation in host media [12–14]. Fig. 4 shows the variation in the normalized probe beam transmission with time, for different values of c at 532 nm and at typical value of r 01. For both cases, as c increases, the percentage modulation increases, as it results in increased absorption of probe laser beam by excited-state molecules. For case (i) (inset of Fig. 4), for c=10 and 200, the NTPI gets modulated by 19.34% and 95.83%, with off time of ~90 and 106 ps, respectively, and on time of 6 and 9 ns, respectively, for peak pumping intensity I m0 V =10 GW/cm2 at 532 nm. For case (ii), 95.99% modulation of probe beam at 532 nm is achieved at I m0 V =1 GW/cm2 for c=150. The off and on times for this case are 103 and 20 ns, respectively. The percentage modulation saturates after a certain value of r 12 at 532 nm.

The same switching contrast is achieved at lower value of c (=150) in case (ii) than in case (i) (c=200). The ground state absorption cross-section (r 01) and relaxation time s 1 of S 1 state at pump wavelength also affect the switching characteristics. Higher values of r 01 result in higher percentage modulation, due to increase in the population of the excited state. An increase in s 1 results in increase in switching time with no change in switching contrast. There is no effect of s 2 as it is very small (~ps). The switching characteristics, with the pump intensity as input and NTPI as output conforms to an all-optical inverter (NOT logic operation). The switching characteristics have been used to design all-optical universal NOR

Fig. 4. Variation of NTPI at 532 nm with time for different values of c, for case (ii) with PD3 concentration of 142 AM at I m0 V =1 GW/cm2. The inset shows the corresponding variation for case (i) with PD3 concentration of 198 AM, Dt=30 ps, I m0 V =10 GW/cm2.

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and NAND logic gates with multiple pulsed pump laser beams for both cases (i) and (ii). For this, the rate equations have been solved by considering two pulsed pump laser beams with I m0 V =10 MW/cm2 at 532 nm for case (i) and I m0 V =0.3 MW/cm2 at 650 nm for case (ii). Amplitude modulation of the cw probe laser beam at 532 nm is considered as output and the two pulsed pump laser beams for respective cases as the two inputs 1 and 2, are shown in Fig. 5(a)–(c). For the all-optical NOR logic gate, the output is low when either one or both the pulses are present and is high when none of the two pulses is present, as is shown in Fig. 5(a)–(c). The presence of two input pulses simultaneously results in increased absorption of probe beam. The same configuration can also result in an all-optical NAND logic gate by considering a threshold level shown by the dotted line in Fig. 5(a). In this case, the output can be considered to be high when either one or none of the input pulses is present and low only when both the input pulses are present simultaneously [15–18]. The switching contrast can be enhanced by increasing r 12p. The percentage modulation also increases with

Fig. 5. All-optical logic operations: (a) NOR gate (without threshold) and NAND gate (with threshold), with variation of NTPI at 532 nm as output with time, case (i) (dotted lines) and case (ii) (solid lines); (b) and (c) are normalized pulse profiles of the two inputs 1 and 2 for both case (i) and (ii).

V and saturates after a certain value. Hence, increase in I m0 the difference between the minima in the output NTPI for single and double input pulses decreases, for designing the NAND logic gate. There is thus an optimum value of I m0 V for which the difference in the output NTPI for the two input pulses and the threshold intensity level is maximum. The results demonstrate the applicability of PD3 molecules for switching applications. Since the properties of PDs can be tailored by various techniques [12–14], the switching characteristics and the operation of the logic gates can be optimized for desired applications. The results would be useful for all-optical signal processing and computing due to simple digital operation.

4. Conclusion All-optical switching in PD3 in two host media (i) ethanol and (ii) PUA has been analyzed in detail based on excited-state absorption to achieve high switching contrast and low switching time. The switching characteristics have been shown to be sensitive to various parameters such as concentration of dye molecules, pump pulse width (Dt), peak pumping intensity (I m0 V ), absorption cross-section of the excited state at 532 nm (r 12) and lifetime of excited state (s 1). It has been shown that there is an optimum value of concentration of PD3 for particular value of I m0 V at which maximum modulation can be achieved. The optimum concentration decreases as I m0 V increases. The switch on/ off time and switching contrast increase with increase in pulse width (Dt), with the modulation level saturating after a certain value. The percentage modulation increases with increase in I m0 V as it results in increase in the number of excited molecules and after a particular value of I m0 V it saturates. A higher switching contrast at relatively lower I m0 V values at 650 nm can be achieved in comparison to pump beam at 532 nm. By considering the pump beam at wavelength corresponding to large value of c 1, higher modulation can be achieved at relatively lower powers due to increased absorption of pump by S0 state that results in higher population of S1 state. The switching contrasts also increases by increasing the absorption cross-section values of excited and ground states at probe and pump wavelengths, respectively. The percentage modulation saturates after a certain value of excited state absorption cross-section at 532 nm. Switching time can be decreased by decreasing the relaxation time of S1 state. The results would be useful in tailoring and optimizing the characteristics of PD3 for device applications. Further, the results have been used to design all-optical NOT and the universal NOR and NAND logic gates with multiple pump laser pulses, that are the basic building blocks of computing circuits. The proposed designs would be useful in optical computing due to high switching contrast, small size, simple digital operation and flexibility.

P. Sharma et al. / Thin Solid Films 477 (2005) 42–47

Acknowledgements P.S. is thankful to Council of Scientific and Industrial Research, India, for the award of Junior Research Fellowship. S.R. is grateful to All India Council for Technical Education, Govt. of India, for Career Award for Young Teachers and to the Department of Science and Technology for partial support of this work.

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